When a $J$-shaped conducting rod is rotating in its own plane with constant angular velocity $\omega$,about one of its ends $P$,in a uniform magnetic field $\vec B$ directed normally into the plane of the paper,then the magnitude of the emf induced across it will be:

• A
  $B\omega \sqrt {{L^2} + {l^2}} $
• B
  $\frac{1}{2}B\omega {L^2}$
• C
  $\frac{1}{2}B\omega ({L^2} + {l^2})$
• D
  $\frac{1}{2}B\omega {l^2}$